A new soft union set: characterizations of hemirings

作者：Zhan, Jianming^*; Dudek, Wieslaw A.; Neggers, J.

来源：International Journal of Machine Learning and Cybernetics, 2017, 8(2): 525-535.

DOI：10.1007/s13042-015-0343-8

• Soft set
• Soft intersection-union product (sum)
• (M, N)-SU-hemiring
• (M, N)-SU-h-ideal
• h-hemiregular hemiring
• h-duo hemiring

Molodtsov's soft set theory provides a general mathematical framework for dealing with uncertainty. The aim of this paper is to lay a foundation for providing a new soft algebraic tool in considering many problems that contain uncertainties. In order to provide these new soft algebraic structures, we introduce the concepts of (M, N)-soft union hemirings and (M, N)-soft union h-ideals, which are generalizations of soft union hemirings and soft union h-ideals. Using a new ordered relation and a soft intersection product (sum), we obtain some related properties. In particular, a new quotient hemiring by a (M, N)-SU-hemiring is constructed. Finally, we investigate some characterizations of h-hemiregular and h-duo hemirings by (M, N)-SU-h-ideals.

• 出版日期2017-4
• 单位湖北民族大学